Differential equations for recovery of the average differential susceptibility of superconductors from measurements of the first harmonic of magnetization

In the paper, inhomogeneous differential equations are obtained to reconstruct the average differential susceptibility of type-II superconductors from the in-phase (real) component of the magnetization’s first harmonic in the hysteresis case. Basing on the second-order differential equation, mathematical modeling of the average differential susceptibility for the theoretical and experimental dependence of the real part of the magnetization’s first harmonic is performed. The Cauchy problem was solved numerically by the Runge-Kutta method of the fourth order of accuracy. To do this, the differential equation for the restoration of the average susceptibility was reduced to a system of differential equations. On the basis of the method developed in the work, the average differential susceptibility of a disc-shaped polycrystalline superconductor ${Y}{Ba_2}{Cu_3}{O_{7-x}}$ was reconstructed from the experimentally obtained first harmonic of magnetization in interval of magnetic fields from 0 to 800 Oe.